Based on the recent free electron model for cohesion in narrow metallicconstrictions by Stafford et al., we calculate the quantum fluctuations in thecohesive force versus elongation. The fluctuations are dominated by states nearthe Fermi energy, thus explaining their apparently universal magnitude of orderepsilon_F/lambda_F. We present numerical results for the force fluctuations ina simple geometry and show that they are well described by the contributions ofa few classical periodic orbits in the Balian-Bloch trace formula for thedensity of states of transverse motion.
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